Question

THEOREM 7.1 , class9 ....... ASA congruence rule
Two triangles are congruent if two angles and the
included side of one triangle are equal to two angles
and the included side of other triangle.. .... help me​

Answer 1

Answer in attachment. Hope it Helps!

Answer 2

Given:

In ΔABC & ΔDEF

∠B = ∠E

∠C = ∠F

BC = EF

To Prove:

ΔABC≅ΔDEF  by ASA congruency rule

Proof:

1) Case 1:

Let AB = DE

In ΔABC & ΔDEF

AB = DE ( assumed)

∠B = ∠E (given)

BC = DE (given)

so, ΔABC ≅ ΔDEF ( By SAS rule)

2) Case 2:

AB > DE

• Construction: take a point M on AB such that MB = DE

In ΔPBC & ΔDEF

MB = DE ( assumed)

∠B = ∠E (given)

BC = DE (given)

so, ΔMBC ≅ ΔDEF ( By SAS rule)

=> ∠MCB = ∠DFE

• But it is given that the ∠ACB = ∠DFE

so ∠ACB = ∠MCB

• This is possible only when point M coincides with A

=> AB = DE

∴ by case 1

ΔABC ≅ ΔDEF

3) Case 3:

AB < DE

• Construction: Take a point N on DE such that EN = AB

• Now follow the case 2 again for AB < DE

• hence we get ΔABC ≅ ΔDEF

In all the cases the triangles are congruent to each other.